HIGH-RESOLUTION RADIO CONTINUUM MEASUREMENTS OF THE NUCLEAR DISKS OF Arp 220

We present new Karl G. Jansky Very Large Array radio continuum images of the nuclei of Arp 220, the nearest ultraluminous infrared galaxy. These new images have both the angular resolution to study the detailed morphologies of the two nuclei that power the galaxy merger and sensitivity to a wide range of spatial scales. At 33 GHz, we achieve a resolution of 0.'' 081 x 0.'' 063 (29.9 x 23.3 pc) and resolve the radio emission surrounding both nuclei. We conclude from the decomposition of the radio spectral energy distribution that a majority of the 33 GHz emission is synchrotron radiation. The spatial distributions of radio emission in both nuclei are well described by exponential profiles. These have deconvolved half-light radii (R-50d) of 51 and 35 pc for the eastern and western nuclei, respectively, and they match the number density profile of radio supernovae observed with very long baseline interferometry. This similarity might be due to the fast cooling of cosmic rays electrons caused by the presence of a strong (similar to mG) magnetic field in this system. We estimate extremely high molecular gas surface densities of 2.2(-1.0)(+2.1) x 10(5) (east) and 4.5(-1.9)(+4.5) x 10(5) (west) M circle dot pc(-2), corresponding to total hydrogen column densities of N-H = 2.7(-1.2)(+2.7) x 10(25) (east) and 5.6(-2.4)(+5.5) x 10(25) cm(-2) (west). The implied gas volume densities are similarly high, n(H2) similar to 3.8(-1.6)(+3.8) x 10(4) (east) and similar to 11(-4.5)(+12) x10(4) cm(-3) (west). We also estimate very high luminosity surface densities of Sigma(IR) similar to 4.2(-0.7)(+1.6)x10(13) (east) and Sigma(IR) similar to 9.7(-2.4)(+3.7)x10(13) (west) L circle dot kpc(-2), and star formation rate surface densities of Sigma(SFR) similar to 10(3.7 +/- 0.1) (east) and Sigma(SFR) similar to 10(4.1 +/- 0.1)(west) M circle dot yr(-1)kpc(-2). These values, especially for the western nucleus are, to our knowledge, the highest luminosity surface densities and star formation rate surface densities measured for any star-forming system. Despite these high values, the nuclei appear to lie below the dusty Eddington limit in which radiation pressure is balanced only by self-gravity. The small measured sizes also imply that at wavelengths shorter than lambda= 1 mm, dust absorption effects must play an important role in the observed light distribution while below 5 GHz free-free absorption contributes substantial opacity. According to these calculations, the nuclei of Arp 220 are only transparent in the frequency range similar to 5-350 GHz. Our results offer no clear evidence that an active galactic nucleus dominates the emission from either nucleus at 33 GHz.